A Digit-Serial Algorithm for the Discrete Logarithm Modulo 2^k

Authors:
Alex Fit-Florea;David W. Matula
Affiliations:
Southern Methodist University;Southern Methodist University
Venue:
ASAP '04 Proceedings of the Application-Specific Systems, Architectures and Processors, 15th IEEE International Conference
Year:
2004

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Abstract

We introduce as our main result a digit-serial residue arithmetic algorithm for computing the discrete logarithm modulo 2^k (dlg)."Digit inheritance" is presented as a fundamentalproperty common to the primitive operations modulo 2^k of addition, multiplication, multiplicative inverse, exponentiation and discrete logarithm.Our main algorithm computes dlg using binary arithmetic with 3 as the logarithmic base and has a critical path containing one modulo 2^k multiplication operation for each of its k iterations.Extensions of the algorithm to other logarithmic bases and computations using digits in a higher radix 2^r are also described.